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%I #21 Sep 08 2022 08:44:39
%S 1,0,1,1,2,3,5,8,13,21,33,54,86,139,223,359,577,928,1492,2399,3858,
%T 6203,9975,16039,25791,41471,66685,107228,172421,277250,445813,716860,
%U 1152698,1853519,2980426,4792474,7706215
%N Expansion of 1/(1-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9).
%C Number of compositions of n into parts p where 2 <= p < = 9. [_Joerg Arndt_, Jun 24 2013]
%H Vincenzo Librandi, <a href="/A013986/b013986.txt">Table of n, a(n) for n = 0..1000</a>
%H R. Mullen, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Mullen/mullen2.html">On Determining Paint by Numbers Puzzles with Nonunique Solutions</a>, JIS 12 (2009) 09.6.5
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 1, 1, 1, 1, 1, 1, 1).
%F a(0)=1, a(1)=0, a(2)=1, a(3)=1, a(4)=2, a(5)=3, a(6)=5, a(7)=8, a(8)=13, a(n)=a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6)+a(n-7)+a(n-8)+a(n-9). - _Harvey P. Dale_, Dec 17 2013
%t CoefficientList[Series[1 / (1 - x^2 - x^3 - x^4 - x^5 - x^6 - x^7 - x^8 - x^9), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 24 2013 *)
%t CoefficientList[Series[1/(1-Total[x^Range[2,9]]),{x,0,40}],x] (* or *) LinearRecurrence[{0,1,1,1,1,1,1,1,1},{1,0,1,1,2,3,5,8,13},40] (* _Harvey P. Dale_, Dec 17 2013 *)
%o (Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9))); // _Vincenzo Librandi_, Jun 24 2013
%Y See A000045 for the Fibonacci numbers.
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_.
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